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Octant-Based Stencil Selection for Meshless Finite Difference Methods in 3D

  • Oleg Davydov
  • Dang Thi OanhEmail author
  • Ngo Manh Tuong
Original Article
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Abstract

We study a simple meshless stencil selection algorithm in 3D for supporting the meshless finite difference method based on radial basis functions (RBF-FD) to solve the Dirichlet problem for the Poisson equation. Our numerical experiments show that the proposed method produces solutions that differ very little from the solutions by the finite element method with Courant’s piecewise linear basis functions, when the domain is discretized by the vertices of the respective tetrahedral triangulation.

Keywords

RBF-FD Meshless methods Generalized finite differences 

Mathematics Subject Classification (2010)

65M06 65N06 

Notes

Acknowledgements

This paper was supported by Thai Nguyen University under grant number DH2015-TN07-03. We are grateful to three anonymous referees for their useful suggestions that have helped to improve our paper.

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GiessenGiessenGermany
  2. 2.Division of Science-Technology & International CooperationThai Nguyen University of Information & Communication Technology, Quyet Thang WardThai Nguyen CityVietnam
  3. 3.Department of Basic SciencesThai Nguyen University of Information & Communication Technology, Quyet Thang WardThai Nguyen CityVietnam

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